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Eighth Mississippi State - UAB Conference on Differential Equations & Computational Simulations
May 7-9, 2009
Department of Mathematics and Statistics, Mississippi State University
Mississippi State, MS, USA

Organizers
Mississippi State University & University of Alabama - Birmingham

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Continuous Dependence Results for Ill-Posed Evolution Problems
by
Matthew Fury
Bryn Mawr College
Coauthors: Rhonda Hughes (Bryn Mawr College)

We prove Hölder-continuous dependence results for the difference between certain ill-posed and approximate well-posed evolution problems. Specifically, given a positive self-adjoint operator D in a Hilbert space, we consider the ill-posed evolution problem du(t)/dt = A(t,D)u(t), u(0) = χ, 0 ≤ t < T. We determine functions f for which solutions of the well-posed problem dv(t)/dt = f(t,D)v(t), v(0)= χ, 0 ≤ t < T approximate known solutions of the original ill-posed problem, thereby establishing continuous dependence on modeling for the problems under consideration.

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Date received: March 25, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxp-73.